• 主题
高级搜索  >
历史搜索 清空历史
首页> 外文期刊>Statistics and computing >Introduction to 'Quantitative bounds of convergence for geometrically ergodic Markov Chain in the Wasserstein distance with application to the Metropolis adjusted Langevin algorithm' by A. Durmus, E. Moulines
【24h】

Introduction to 'Quantitative bounds of convergence for geometrically ergodic Markov Chain in the Wasserstein distance with application to the Metropolis adjusted Langevin algorithm' by A. Durmus, E. Moulines

机译：A. Durmus，E. Moulines所著的“ Wasserstein距离上的几何遍历马尔可夫链的收敛量化界及其在大都会调整的Langevin算法中的应用”简介

获取原文
获取原文并翻译 | 示例
       
页面导航
  • 摘要
  • 著录项
  • 相似文献
  • 相关主题

摘要

The Wasserstein distance between probability distributions might be intuitively described as a minimal effort required to map one distribution onto another. The concept has a long history with connections to optimal transport theory. However, the applications on convergence properties of Markov chains are more recent. The present paper contains interesting theoretical work applying recently developed techniques based on the Wasserstein metric for analysing the rate of convergence of geometrically ergodic Markov chains. Bounds on the Wasserstein distances are also based on a drift condition but minorization conditions are replaced by the existence of a coupling set, together with appropriate conditions on the transition kernel. A 'natural' coupling for MCMC algorithms is achieved simply by running two versions of an algorithm with the same random numbers. The main results of the paper can be useful in general when quantifying the (worst-case) convergence of MCMC algorithms to the equilibrium. It appears that at least in certain cases the Wasserstein techniques can provide much tighter upper bounds for the rate of convergence than earlier results which are based on drift and minorization inequalities.
机译：概率分布之间的Wasserstein距离可以直观地描述为将一种分布映射到另一种分布所需的最小工作量。这个概念与最佳运输理论有着悠久的历史。然而，关于马尔可夫链的收敛性的应用是最近的。本文包含有趣的理论工作，这些工作运用基于Wasserstein度量的最新开发技术来分析几何遍历马尔可夫链的收敛速度。 Wasserstein距离上的边界也基于漂移条件，但是最小化条件被耦合集的存在以及过渡核上的适当条件所代替。仅通过运行具有相同随机数的两种算法版本，即可实现MCMC算法的“自然”耦合。当量化MCMC算法（最坏情况）收敛到平衡时，本文的主要结果通常会很有用。似乎至少在某些情况下，Wasserstein技术可以为收敛速度提供比基于漂移和极小化不等式的早期结果更紧密的上限。

著录项

  • 来源
    《Statistics and computing》 |2015年第1期|3-3|共1页
  • 作者

    Heikki Haario;

  • 作者单位

    Faculty of Technology, Lappeenranta University of Technology, Lappeenranta, Finland;

  • 收录信息
  • 原文格式 PDF
  • 正文语种 eng
  • 中图分类
  • 关键词

相似文献

  • 外文文献
获取原文

客服邮箱：kefu@zhangqiaokeyan.com

京公网安备：11010802029741号 ICP备案号：京ICP备15016152号-6 六维联合信息科技 (北京) 有限公司©版权所有

  • 客服微信

  • 服务号